I've been dealing w/ a lot of heatsink issues in my new (horribly designed) 3630, so this I know well

1) You cannot evaluate the "stock heatsink" for the CPU without comparing the TDP of whatever it came with and the proposed new chip. What CPU do you have now?

The TDP of the chip determines the proper heatsink (bigger is better of course).  If it shipped with the original system then it is probably fine (you may need to repaste) though it may be loud and you may not be able to OC.  Run a chip temp test and you'll see what's up.

2) I'm not a complete gaming expert, but as a general rule you are better off spending money on a card than a chip, so you may not need to bother with adding a CPU riser (or changing your CPU) at all.

3) See spec sheet @ https://www.dell.com/downloads/global/products/precn/en/dell_precision_t5500_specsheet.pdf

Your original WS looks like it was specified for two cards of and you can see the cards available and compare their power draw to the proposed 750 or 1050ti.  My gut says you're fine though you should check.

4) additional fans will give you more headroom for temperature and may help keep the system a bit quieter overall.

I just found that the tdp of the xeon e5520 cpu is 80w, and the xeon 5687 is 130w. Do you think this difference justify's getting a better heatsink?

Thank you for your reply. I haven't booted the system up yet because it doesn't have any ram or hard drives in it yet. I was able to find what the CPU is, its a Intel Xeon E5520. It says its 2.26 ghz so I think a upgrade to the 3.6 ghz CPU would be a significant improvement. I'm not sure what the tdp is compared to the newer CPU but I would be willing to upgrade the heatsink if that's required to keep it cool. I feel like the new GPU would be fine since it would be the only one running and doesn't require much power. I don't want to destroy it with newer hardware because I didn't have sufficient cooling for it, so i'm trying to play it safe. Again, thank you for your response. 

If your current HS is similar to this w/ a single fan blowing down onto a finned aluminum plate

it WILL NOT support 130w. 130W requires a larger heatsink and often two fans, look for cpu coolers on newegg. 

If your heatsink and cooler look very different you may be OK, but the only way to make sure would be to dig up old spec sheets and manuals.  If both these things are true then your heat sink should be fine:

a) If Dell offered a 130W TDP processor as an available option on your WS (look at processor models and google them)

AND IF

b) Dell only installed a single type of heatsink and fan design, so that you have evidence the installed heatsink was designed for a 130W TDP processor.

IMO, if you are gaming only, and if you have to spend the non-inconsiderable $$$ to upgrade both the processor and heatsink, you'll probably be better off spending the money on your video card. The Passmark differential on those CPUs is not very large.  But I'm not a serious gamer so I may be wrong, you should check tomshardware forums.

Thank you for the feedback. I had a feeling that was the case, and i will look into getting a different heatsink. 

Hi Billy, I'm doing the same thing now I was wondering if you ended up getting a suitable cooler. The space is really tight in there!  

Thanks!

Yeah I found one on ebay. They look higher quality than the original aluminum one. Here's a picture of the one I got and it works great

Btw if your going to put a new GPU in there then get an extra 80mm case fan with a molex connector, otherwise I think it will get too hot

Thanks a lot! I'll get auxiliary fans too!